For some reason tethering doesn't seem to work worth a damn.
I have the T-Mo S4 and the built-in T-Mo tethering app simply does not work. And I can't find the WiFi Tether for Root Users app on the store because my device is filtered. I guess I'll go download the APK from somewhere and see how that works.
But honestly, the internet on the phone just *works*. I would be easier just to stream NetFlix or Hulu video stream from the Android to the laptop.
The problem is that the laptop is just not built to be a device that accepts video inputs, as frustrating as that is.
Since you're on T-Mobile, and I'm guessing you're on either 2.5GB unlimited data, you should have 2.5GB of supported tethering. Calling T-Mobile support for why the tethering doesn't work is probably your best bet. A galaxy S4 should be supported, and it may be something as simple as needing a different SIM card.
If you would really rather just have an external monitor for your cell, though, you may have to buy a monitor specifically for that purpose.